Solve simple linear-quadratic systems algebraically and graphically.
Solve a linear-quadratic system by substituting the line into the quadratic
Problem
Solve the system \(y=x^{2}\) and \(y=x+2\) by substitution. Equate the two expressions for \(y\), solve every resulting \(x\)-value, and substitute back to form the complete ordered-pair set.
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What this problem is really about
At an intersection, the line and parabola have the same y-value, so their right sides can be equated. We’ll solve the resulting quadratic for every x-value, substitute each one back into a convenient equation for y, and report the complete ordered-pair set.
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